I'm not sure how this tree got here. I don't think it was planted so may be it's a result of an Apple core being thrown in the bushes but it's here, and the fruit is edible.
The trouble is that it's now too tall to harvest the apples, and to spray it to treat the Apple scab. The height is the same as the one storey house it's beside.
What sort of pruning is still possible to bring the branches to reachable height?
I'm thinking of making these cuts while it is still winter.
If it is born from a seed, it should be more resistant from disease. In any case you can check if there are sign of graft on lower trunk. There are many apples in the tree (and large) so you were lucky (or it is a grafted plant).
About pruning: the main problem I see: there is many other plants near the apple. Ideally it should have not taller plant for few meters in every direction. For this reason, I find difficult to prune as you want. I would start a normal pruning, but on the higher part of the plant. Remove the central shots, to force the plant to growth laterally. On apple tree there are two kind of pruning: normal, and one to "rejuvenate", that mean that you can short the apple tree (maybe within few years). You still have some branches on lower plant. With some trimming on the upper part, the lower branches could growth better (and create new branches).
But for me, there is too many plant nearby. You should consider to have less plants.
First things first, why would you want to cut the three main branches of this tree? What you need to do is to remove any dead or diseased limbs and remove any branches facing outward.
Also, keep in mind that any cut on a tree is like a wound, you should definitely NOT cut the tree at those lines! They are too far from the trunk! Trees do have the ability to heal themselves, given a chance, of course. The angle of the cut is important as well, as you don't want to create a place for water to rest (and cause disease).
Lastly, be sure to use clean tools that are appropriate for the size of the branches.
Have you ever heard of Pollarding?
Pollarding is a pruning system in which the upper branches of a tree are removed, promoting a dense head of foliage and branches. It has been common in Europe since medieval times and is practised today in urban areas worldwide, primarily to maintain trees at a predetermined height.
As far as I know there is no reason to believe that this tree would act any differently. Simply wait until the winter season and then make your cuts. If you want the new growth to adopt a signature look then your going to need a lot of wire and a bit of effort. Draw the new growth in the direction you want it to grow with wire and rope.
Trees are super resilient once they grow a solid root stock. There is no reason to believe you couldn't cut his tree on its main shoot and graft a whole new apple tree to it if you wished.
This extract on how to renovate fruit trees is from Cavendish Encyclopedia of Pruning and Training by Christopher Brickell and David Joyce, my go-to book for all pruning questions.
"In the first year, remove dead, diseased and damaged wood. Remove, or shorten to a replacement shoot or branch, crowded and crossing branches. In the second year, improve fruiting potential: shorten overlong and unproductive growth to a replacement shoot and thin regrowth from the sites of previous cuts. On apples and pears, reduce congested spur systems."
While it's not specifically for reducing the size of the tree, one benefit of this method is that you may get replacement shoots after the first year that will show you where to make your second year cuts.
The time of year is late winter or early spring.
Like you, I've been told not to remove more than 25% in a given year, but this implies it can be done in two years.
